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Explanation:

Let us choose a town, say A.
If I were to consider this as the base town and construct two roads such that I connect any pair of towns, I get
the following combinations:
1. AB – BC, 2. AB – BD, 3. AC – CB, 4. AC – CD,
5. AD – DB and 6. AD – DC.
From any of these combinations, if I were to construct a road such that it again comes back to A, then it would form a triangle.
To avoid a triangle, the third road that I construct should not be connected to A but to the third town.
Hence, the combination would be:
1. AB – BC – CD, 2. AB – BD – DC, 3. AC – CB – BD,
4. AC – CD – DB, 5. AD – DB – BC and 6. AD – DC – CB.
Thus, from each town, we can construct 6 such combinations.
Hence, total number of combinations that we can have from four towns = (6 × 4) = 24.